JAKARTA, Indonesia — Both candidates claimed victory Wednesday in Indonesia’s presidential election, the tightest race since the former Southeast Asian dictatorship made the transition to democratic politics less than two decades ago.

Joko Widodo, the popular chief executive of the capital city, Jakarta, said he had won based on samples of votes being counted at 480,000 polling stations nationwide that gave him a lead of between 4 and 6 percentage points. The so-called quick counts have accurately forecast results in the last several national elections.